{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 176 0 0 0 2 0 0 0 
0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 
}{CSTYLE "Define" -1 256 "Times" 1 12 163 163 163 0 1 1 0 0 0 0 0 0 0 
1 }{CSTYLE "Emphasis" -1 257 "Times" 1 12 128 0 128 1 0 0 0 0 0 0 0 0 
0 1 }{CSTYLE "normal C" -1 258 "Times" 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 
1 }{CSTYLE "Menu" -1 259 "" 0 0 163 163 163 0 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 260 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
261 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 1 10 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 10 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 266 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
267 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 10 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 1 10 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 271 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
272 "" 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 1 10 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "Geneva" 1 10 0 0 0 1 0 
0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Geneva" 
1 10 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }
{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Monaco" 1 9 255 0 0 1 
2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 0" 
-1 257 1 {CSTYLE "" -1 -1 "Geneva" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }
1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 2" -1 258 1 {CSTYLE "" 
-1 -1 "Geneva" 1 10 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 
2 2 0 1 }}
{SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT 257 41 "COMPLEX ANALYSIS: Maple
 Worksheets,  2001" }{TEXT 272 144 "\n(c) John H. Mathews          Rus
sell W. Howell\nmathews@fullerton.edu     howell@westmont.edu\n\nCompl
imentary software to accompany the textbook:" }}{PARA 257 "" 0 "" 
{TEXT 257 82 "COMPLEX ANALYSIS: for Mathematics & Engineering, 4th Ed,
 2001, ISBN: 0-7637-1425-9" }{TEXT 271 197 "\nJones and Bartlett Publi
shers, Inc.,      40  Tall  Pine  Drive,      Sudbury,  MA  01776\nTel
e.  (800) 832-0034;      FAX:  (508)  443-8000,      E-mail:  mkt@jbpu
b.com,      http://www.jbpub.com/" }}}{EXCHG {PARA 257 "" 0 "" {TEXT 
266 1 "\n" }{TEXT 256 65 "CHAPTER 4  SEQUENCES, JULIA and MANDELBROT S
ETS, and Power Series" }{TEXT 273 2 "\n\n" }{TEXT 256 38 "Section 4.2 \+
 Julia and Mandelbrot Sets" }}{PARA 257 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 274 97 "Load Maple's  \"densityplot\" pro
cedure.\nMake sure this is done only ONCE during a Maple  session.\n" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }{TEXT -1 0 "" }}}
{EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT 256 
13 "The Julia set" }{TEXT 268 1 "\n" }}{PARA 257 "" 0 "" {TEXT 260 4 "
The " }{TEXT 257 9 "Julia set" }{TEXT 269 65 " associated to a complex
 number c is found by iterating the map  " }{XPPEDIT 18 0 "z = z^2 + c
" "6#/%\"zG,&*$F$\"\"#\"\"\"%\"cGF(" }{TEXT 261 109 " .  \nThe set of \+
points that do not escape to infinity is the Julia set.\n\nHere is the
 Julia set generated by  " }{XPPEDIT 18 0 "c = -1.25 + 0 i" "6#/%\"cG,
&-%&FloatG6$\"$D\"!\"#!\"\"*&\"\"!\"\"\"%\"iGF.F." }{TEXT 264 237 " .
\n\nThis is a fuzzy picture of Color Plate 4.\nIncrease the number of \+
grid points to get a sharper picture.  Also, it will increase the comp
uting \ntime, and the memory required is 3,557K.  It takes quite a bit
 of time with  grid=[50,50].\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "
juliaC := proc(X,Y)\n  local Z, ct;\n  Z := X + I*Y;\n  for ct from 1 \+
while ct<25 and evalf(abs(Z))<2.0 \n    do\n      Z := Z^2 + (-1.25)\n
    od;\n  -ct;\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "d
ensityplot('juliaC'(x,y),\n  x=-1.5..1.5, y=-1.5..1.5,\n  grid=[100,10
0],\n  scaling=constrained,\n  style=PATCHNOGRID, axes=NONE);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 257 "" 0 "" 
{TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT 256 18 "The Mandelbrot Set" }
{TEXT 267 6 "\n\nThe " }{TEXT 257 14 "Mandelbrot set" }{TEXT 270 82 " \+
is the set of points c that do not escape to infinity under iteration \+
of the map\n" }{XPPEDIT 18 0 "c = c^2 + c" "6#/%\"cG,&*$F$\"\"#\"\"\"F
$F(" }{TEXT 262 342 " .   Points in the Mandelbrot set have connected \+
\nThis modification of the juliaC code can be used to plot the Mandelb
rot set.\n\nThis is a fuzzy picture of Color Plate 6.\nIncrease the nu
mber of grid points to get a sharper picture.  Also, it will increase \+
the computing \ntime and the memory.  It takes quite a bit of time wit
h   grid=[50,50].\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 160 "mandelbrotC
 := proc(X,Y)\n  local Z, ct;\n  Z := X + I*Y;\n  for ct from 1 while \+
ct<50 and evalf(abs(Z))<2.0 \n    do\n      Z := Z^2 + (X + I*Y)\n    \+
od;\n  -ct;\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "densi
typlot('mandelbrotC'(x,y),\n  x=-2..0.55, y=-1.15..1.15,\n  grid=[100,
100],\n  scaling=constrained,\n  style=PATCHNOGRID, axes=NONE);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 257 "" 0 "" {TEXT 263 19 "End of Section
 4.3." }}}}{MARK "0 0 0" 12 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }